What is the cross product of [3,1,-4] and [1,1,18]

Find the vectors T, N, and B at the given point.
$r(t)=<t^2,\frac{2}{3}{t}^3,t>$ and point $<4,-\frac{16}{3},-2>$

Find a nonzero vector orthogonal to the plane through the points P, Q, and R. and area of the triangle PQR
Consider the points below
P(1,0,1) , Q(-2,1,4) , R(7,2,7)
a) Find a nonzero vector orthogonal to the plane through the points P,Q and R
b) Find the area of the triangle PQR

Find the volume of the parallelepiped with one vertex at the origin and adjacent vertices at ${\displaystyle (1,3,0),(-2,0,2),\text{and}(-1,3,-1)}$.

How to calculate the intersection of two planes ?
These are the planes and the result is gonna be a line in ${\displaystyle {\mathbb{R}}^3}$:
${\displaystyle x+2y+z-1=0}$
${\displaystyle 2x+3y-2z+2=0}$

What are the standard three-dimensional unit vectors?

How do you find the inner product and state whether the vectors are perpendicular given ${\displaystyle <8,4>\cdot <2,4>}$

Find the best approximation to z by vectors of the form ${\displaystyle c_1{v}_1+c_2{v}_2}$
$z=\left[\begin{array}{c}3\\ -7\\ 2\\ 3\end{array}\right],v_1=\left[\begin{array}{c}2\\ -1\\ -3\\ 1\end{array}\right]v_2=\left[\begin{array}{c}1\\ 1\\ 0\\ -1\end{array}\right]$